In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic forward investment performance processes (power, exponential and logarithmic). We develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive control problem. We also develop a connection, fo...

To a given reference triangle Δ and three directions α, β, γ we construct four triads of homothetic triangles and investigate relations between their homothetic centers, centroids, midway triangles, medial triangles and areas. 1. Two triads of homothetic triangles Given an arbitrary triangle Δ = ABC with sidelines a, b, c and an ordered set {α, β, γ} of three directions in the plane of Δ. Let p...

Nonempty sets X1 and X2 in the Euclidean space R n are called homothetic provided X1 = z+λX2 for a suitable point z ∈ R n and a scalar λ 6= 0, not necessarily positive. Extending results of Süss and Hadwiger (proved by them for the case of convex bodies and positive λ), we show that compact (respectively, closed) convex sets K1 and K2 in R n are homothetic provided for any given integer m, 2 ≤ ...

For a change in prices, the common-scaling social cost-of-living index is the equal scaling of each individual’s expenditure level needed to restore the level of social welfare to its prechange value. This index does not, in general, satisfy two standard index-number tests. The reversal test requires the index value for the reverse change to be the reciprocal of the original index. And the circ...

Representations of planar triangulations as contact graphs of a set of internally disjoint homothetic triangles or respectively of a set of internally disjoint homothetic squares have received quite some attention in recent years. In this paper we investigate representations of planar triangulations as contact graphs of a set of internally disjoint homothetic pentagons. Surprisingly such a repr...

We show a result that can be expressed in any of the following three equivalent ways: 1. All self-scaled barrier functionals for the cone + of symmetric positive semideenite matrices are homothetic transformation of the universal barrier functional. 2. All self-scaled barrier functionals for + can be expressed in the form X 7 ! ?c 1 ln det X + c 0 for some constants c 1 > 0; c 0 2 R. 3. All sel...